A coin with unknown probability p of landing head up when tossed, was tossed until it first landed head up. It happened on the 5th toss. Describe an appropriate statistical model for this experiment and write down the observed Likelihood function L(p).
I assumed this was the same as...
How would you show that {(x,y,z) € R^3 :√11x - √13z=0} is a subspace of R^3?
I know you have to make sure it fits the definition of a subspace, i.e prove
u+v € W
and alpha(v) € W
but I am not sure how you would do this using √11x - √13z=0 ?
Homework Statement
The question states:
Consider the subset S of R^4 given by:
S={(2,3,-1,7), (1,0,1,3), (0,3,-3,1), (12,15,-3,29)}
i) Decide whether the vectors in S form a linearly independent set.
ii) Let V be the vector subspace of R^4 spanned by the vectors of S, i.e:
V=span{...
Homework Statement
Find an example of a continuous function f:R->R with the following property.
For every epsilon >0 there exists a delta >0 such that |f(x)-f(y)| <epsilon whenever x,y e R with |x-y|<delta.
Now find an example of a continuous function f:R->R for which this property does nto...
I have spent ages on this final part of a question but don't seem to be going anywhere - any help would be greatly appreciated!
Given a function f:R->R let X be the set of all points at which f is continuous.
Find an example of a function defined on R which is continuous on Z only.
The question states:
Give two different examples of f:R->R such that f is continuous and satisfies f(x+y)=f(x)+f(y) for every x,y e R. Find all continuous functions f:R->R having this property. Justify your answer with a proof.
I came up with one example:
f(x)=ax
then...
To calculate E[X] I did: ∫xf(x) dx (integral bounds between minus ∞ and ∞ - sorry don't know how to type it properly!)
using integration by parts, i got:
E[x]=[-x/2 e^-2|x|] + [1/4 e^-2|x|] (bounds evaluated between -∞ and ∞)
=(-∞/2 e^-2|∞|) - (∞/2 e^-2|∞|) + (-1/4 e^-2|∞| + 1/4 e^-2|∞|)...
I want to calculate E[x] of the following continuous distribution having density: f(x)=e^-2|x|
for x in the reals (x e R)
I did the calculation with integral bounds infinity and minus infinity, are these the right bounds to use since we are only told x e R?
I got 0 as the answer, can someone...